The proton conductivity mechanism in per-fluorinated sulfonic acid/PTFE copolymer Fumapem® membranes for polymer electrolyte membranes has been investigated. Three samples of Fumapem® F-950, F-1050 and F-14100 membranes with different ion exchange capacity 1.05, 0.95, and 0.71 meq/g, respectively, were used in this study after drying. The o-Ps hole volume size (V_{FV,Ps}) was quantified using the positron annihilation lifetime technique while the proton conductivities (σ ) were measured using LCR Bridge as function of temperature. It was found that as the ion exchange capacity increases, the proton conductivity increases and the free volume expands. Temperature dependences of proton conductivity and the o-Ps hole volume size (V_{FV,Ps}) reflect the glass transition temperature of the membrane. A good linear correlation between the reciprocal of the o-Ps hole volume size (1/V_{FV,Ps}) and log(σ)+Δ E_a/2.303k_{B}T, (where ΔE_a is the activation energy, T is the absolute temperature and k_{B} is the Boltzmann constant) at different temperatures indicate that the ionic motion in dry Fumapem® is governed by the free volume. A linear relationship between the critical hole size γ V*_{i} and the ion exchange capacity was also achieved.